HARTFORD -- It's a rare thing for minority Republicans to get their way in the state House of Representatives, where a 99-52 majority means Democrats can get just about anything they want.

But late Thursday night, toward the end of a 10-hour legislative day, second-term Rep. Gail Lavielle, R-Wilton, succeeded in persuading Democrats to adopt an amendment.

The bill was about fostering innovation in public schools, and Lavielle saw the moment as a good time to help both higher-performing and lower-achieving school districts. The bill passed 135-0 and now heads to the Senate.

"I was pleased at how well it went," said Lavielle, a former corporate executive who is on the legislative Education Committee. "I introduced something very similar last year around this time, but there was not an appetite for it."

The amendment calls for a task force to study the possibility of giving schools relief from expensive state mandates.

Under Lavielle's bill, high-performing schools such as Weston High School and New Canaan High School could have more field trips and laboratory work in lieu of mandatory class time. Group learning and online learning could also replace classroom lessons.

In addition, Lavielle's bill would include the five low-income districts that show the greatest decrease in the achievement gap from July 2010 to July 2012. As a whole, Connecticut has the largest gap in the nation between high-performing and low-performing schools.

Lavielle said that while some legislative task forces can create reports that do nothing but gather dust, her proposed eight-member group appointed by legislative leaders would have a narrow scope and an Oct. 1 deadline.

In 2012, Gov. Dannel P. Malloy created the Red Tape Review and Removal Task Force, which Lavielle said produced a dry report that seems to have gone nowhere, especially on the issue of mandate relief.

An example of her mandate relief would be to allow schools to divert from the so-called common core of classes and create other curriculum options. Another example would be to cut down on reports that many teachers say eat up time that would be better used for instruction.

"I think it's just been long in coming," Lavielle said, adding that it won't cost any money, but it has the potential to save money and resources.

"I was very happy (at the bill's passage in the House)," she said. "It appears to be a sincere desire for collaboration from both sides. This can't be one of those task forces that do nothing."